i studied math a number of years ago but i'm quite interested in math. when i was studying calculus, i was told that for a function to be continuous at x=a, it must be defined at x=a. how can the function in this given question ever be defined at x=0 because its denominator becomes 0 when x=0? my guess is something is amiss in this question.
yes you are right about it. The function will never be defined at x=0. For example take the case of another function G(X)=(x-2)(x-3)/(x-2). This function would also not be defined at x=2 because then the denominator would become 0. although you can take out its limit which is basically the value which you get when a approach a number from both sides( left hand side(2-) and right hand side(2+)) then you would get the answer as -1 by cancelling out the x-2 term. now this question above in the video asks that for the function to be defined at x=0, what value you should assign to f(0) which would basically be its limit when x tends to 0
